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Dynamic power management aims at extending battery life by switching devices to lower-power modes when there is a reduced demand for service. Static power management strategies can lead to poor performance or unnecessary power consumption when there are wide variations in the rate of requests for service. This paper presents a hierarchical scheme for adaptive dynamic power management (DPM) under nonstationary service requests. As the main theoretical contribution, we model the nonstationary request process as a Markov-modulated process with a collection of modes, each corresponding to a particular stationary request process. Optimal DPM policies are precalculated offline for selected modes using standard algorithms available for stationary Markov decision processes (MDPs). The power manager then switches online among these policies to accommodate the stochastic mode-switching request dynamics using an adaptive algorithm to determine the optimal switching rule based on the observed sample path. As a target application, we present simulations of hierarchical DPM for hard disk drives where the read/write request arrivals are modeled as a Markov-modulated Poisson process. Simulation results show that the power consumption of our approach under highly nonstationary request arrivals is less than that of a previously proposed heuristic approach and is even comparable to that of the optimal policy under stationary Poisson request process with the same arrival rate as the average arrival rate of the nonstationary request process.